Re: operators

*To*: mathgroup <mathgroup at yoda.physics.unc.edu>*Subject*: Re: operators*From*: Ronald D. Notestine <ronald at sccs.chukyo-u.ac.jp>*Date*: Tue, 09 Nov 93 03:17:03 +0900

Yes. A good exposition is in a book by Dimitri VVedensky, just published by Addison-Wesley, titled "Partial Differential Equations with Mathematica". I take the following from the introduction: u := {r,theta,phi} h := {1,r,r Sin[theta]} Where the entries must be in the same order. The Jacobian, J, is J = h[[[1]]h[[2]]h[[3]] and the gradient is given by Grad[f_] := Table[D[f,u[[i]]]/h[[i]],{i,3}] and the divergence by Div[f_] := (1/J)Sum[D[(J f[[i]])/h[[i]], u[[i]],{i,3}] I have not used these myself, and retyped them by hand. But, they certainly look correct. Incidentally, I have just noticed that there is also a package "Calculus`VectorAnalysis`" that has all of this and a lot more premade. The package is desscribed in the technical report "guide to Standard Mathematica Packages". We get a copy in every MMA box we get for the Macintosh. Hope this helps. Good luck. Ronald D. Notestine Faculty of Management Chukyo University Nagoya, Japan ronald at sccs.chukyo-u.ac.jp fax: 81-52-835-7196